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International Conference on Theory and Applications of Satisfiability Testing

SAT 2017: Theory and Applications of Satisfiability Testing – SAT 2017 pp 347–363Cite as

Theory Refinement for Program Verification

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10491))

Abstract

Recent progress in automated formal verification is to a large degree due to the development of constraint languages that are sufficiently light-weight for reasoning but still expressive enough to prove properties of programs. Satisfiability modulo theories (SMT) solvers implement efficient decision procedures, but offer little direct support for adapting the constraint language to the task at hand. Theory refinement is a new approach that modularly adjusts the modeling precision based on the properties being verified through the use of combination of theories. We implement the approach using an augmented version of the theory of bit-vectors and uninterpreted functions capable of directly injecting non-clausal refinements to the inherent Boolean structure of SMT. In our comparison to a state-of-the-art model checker, our prototype implementation is in general competitive, being several orders of magnitudes faster on some instances that are challenging for flattening, while computing models that are significantly more succinct.

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Notes

  1. 1.

    We do support these in our implementation, but their results are treated nondeterministically, that is, as unbound variables from \( Sz \).

  2. 2.

    The shift operations \(\mathtt {\,\ll \,}, \mathtt {\,\gg _a\,}, \mathtt {\,\gg _l\,}\) assume a bit-width that is a power of two.

  3. 3.

    OpenSMT2: https://scm.ti-edu.ch/repogit/opensmt2.git, git ID: 99c960e4c; HiFrog (including cbmc that shares the CProver framework [2] with HiFrog): https://scm.ti-edu.ch/repogit/hifrog, git ID b35956f2c.

References

  1. http://verify.inf.usi.ch/hifrog/theoref

  2. http://www.cprover.org/

  3. Alt, L., Asadi, S., Chockler, H., Even Mendoza, K., Fedyukovich, G., Hyvärinen, A.E.J., Sharygina, N.: HiFrog: SMT-based function summarization for software verification. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10206, pp. 207–213. Springer, Heidelberg (2017). doi:10.1007/978-3-662-54580-5_12

    Chapter  Google Scholar 

  4. Alt, L., Fedyukovich, G., Hyvärinen, A.E.J., Sharygina, N.: A proof-sensitive approach for small propositional interpolants. In: Gurfinkel, A., Seshia, S.A. (eds.) VSTTE 2015. LNCS, vol. 9593, pp. 1–18. Springer, Cham (2016). doi:10.1007/978-3-319-29613-5_1

    Google Scholar 

  5. Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999). doi:10.1007/3-540-49059-0_14

    Chapter  Google Scholar 

  6. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011). doi:10.1007/978-3-642-18275-4_7

    Chapter  Google Scholar 

  7. Brady, B.A., Bryant, R.E., Seshia, S.A.: Learning conditional abstractions. In: Proceedings of FMCAD 2011, pp. 116–124. FMCAD Inc. (2011)

    Google Scholar 

  8. Brummayer, R., Biere, A.: Lemmas on demand for the extensional theory of arrays. J. Satisfiability Boolean Model. Comput. 6, 165–201 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Bruttomesso, R., et al.: A lazy and layered SMT(\(\cal{BV}\)) solver for hard industrial verification problems. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 547–560. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73368-3_54

    Chapter  Google Scholar 

  10. Cimatti, A., Griggio, A., Irfan, A., Roveri, M., Sebastiani, R.: Invariant checking of NRA transition systems via incremental reduction to LRA with EUF. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 58–75. Springer, Heidelberg (2017). doi:10.1007/978-3-662-54577-5_4

    Chapter  Google Scholar 

  11. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). doi:10.1007/10722167_15

    Chapter  Google Scholar 

  12. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752–794 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cytron, R., Ferrante, J., Rosen, B., Wegman, M., Zadeck, F.: An efficient method of computing static single assignment form. In: Proceedings of POPL 1989, pp. 25–35. ACM (1989)

    Google Scholar 

  14. Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: a theorem prover for program checking. J. ACM 52(3), 365–473 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Fedyukovich, G., Sery, O., Sharygina, N.: eVolCheck: incremental upgrade checker for C. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 292–307. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36742-7_21

    Chapter  Google Scholar 

  16. Gurfinkel, A., Belov, A., Marques-Silva, J.: Synthesizing safe bit-precise invariants. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 93–108. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54862-8_7

    Chapter  Google Scholar 

  17. Hadarean, L., Bansal, K., Jovanović, D., Barrett, C., Tinelli, C.: A tale of two solvers: eager and lazy approaches to bit-vectors. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 680–695. Springer, Cham (2014). doi:10.1007/978-3-319-08867-9_45

    Google Scholar 

  18. Ho, Y.S., Chauhan, P., Roy, P., Mishchenko, A., Brayton, R.: Efficient uninterpreted function abstraction and refinement for word-level model checking. In: Proceedings of FMCAD 2016, pp. 65–72. ACM (2016)

    Google Scholar 

  19. Hyvärinen, A.E.J., Marescotti, M., Alt, L., Sharygina, N.: OpenSMT2: an SMT solver for multi-core and cloud computing. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 547–553. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_35

    Google Scholar 

  20. Katz, G., Barrett, C., Harel, D.: Theory-aided model checking of concurrent transition systems. In: Proceedings of FMCAD 2015, pp. 81–88. IEEE (2015)

    Google Scholar 

  21. Kroening, D., Strichman, O.: Decision Procedures - An Algorithmic Point of View. Texts in Theoretical Computer Science. An EATCS Series, 2nd edn. Springer, Heidelberg (2016)

    Book  MATH  Google Scholar 

  22. Kutsuna, T., Ishii, Y., Yamamoto, A.: Abstraction and refinement of mathematical functions toward SMT-based test-case generation. Int. J. Softw. Tools Technol. Transf. 18(1), 109–120 (2016)

    Article  Google Scholar 

  23. McMillan, K.L.: An interpolating theorem prover. Theor. Comput. Sci. 345(1), 101–121 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the SNF grants 163001 and 166288 and the SNF fellowship P2T1P2_161971.

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Authors and Affiliations

  1. Università della Svizzera italiana, Lugano, Switzerland

    Antti E. J. Hyvärinen, Sepideh Asadi & Natasha Sharygina

  2. King’s College London, London, UK

    Karine Even-Mendoza & Hana Chockler

  3. University of Washington, Seattle, USA

    Grigory Fedyukovich

Authors
  1. Antti E. J. Hyvärinen
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  2. Sepideh Asadi
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  3. Karine Even-Mendoza
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  4. Grigory Fedyukovich
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  5. Hana Chockler
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  6. Natasha Sharygina
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Corresponding authors

Correspondence to Antti E. J. Hyvärinen , Sepideh Asadi , Karine Even-Mendoza , Grigory Fedyukovich , Hana Chockler or Natasha Sharygina .

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Editors and Affiliations

  1. UNSW Sydney, Sydney, New South Wales, Australia

    Serge Gaspers

  2. University of New South Wales , Sydney, New South Wales, Australia

    Toby Walsh

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Hyvärinen, A.E.J., Asadi, S., Even-Mendoza, K., Fedyukovich, G., Chockler, H., Sharygina, N. (2017). Theory Refinement for Program Verification. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-66263-3_22

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